arXiv subjects
Publications and source records attributed to Thorsten Poeschel.
Large scale computer simulations are presented to investigate the avalanche statistics of sand piles using molecular dynamics. We could show that different methods of measurement lead to contradicting conclusions, presumably due to avalanches not reaching the end of the experimental table.
A novel effect in a granular material under swirling motion of the container is presented. At low packing densities the material rotates in the same direction as the swirling motion of the container (rotation). At higher densities the cluster of granular material rotates in opposite direction (reptation). The change of the direction of the motion of the cluster takes place at a critical packing density while the diffusion coefficient changes significantly. The measured critical density of the packing is in good agreement with results obtained by molecular dynamics simulation.
The properties of dense granular systems are analyzed from a hydrodynamical point of view, based on conservation laws for the particle number density and linear momentum. We discuss averaging problems associated with the nature of such systems and the peculiarities of the sources of noise. We perform a quantitative study by combining analytical methods and numerical results obtained by ensemble-averaging of data on creep during compaction and molecular dynamics simulations of convective flow. We show that numerical integration of the hydrodynamic equations gives the expected evolution for the time-dependent fields.
We investigate the evolution of the velocity distribution function of a granular gas composed of viscoelastic particles in the homogeneous cooling state, i.e. before clustering occurs. The deviation of the velocity distribution function from the Maxwellian distribution is quantified by a Sonine polynomials expansion. The first non-vanishing Sonine coefficient a_2(t), reveals a complex time dependence which allows to assign the granular gas the property of an age. We discuss the possibility to measure the age of a granular gas.
We discuss a new optimization strategy, which considerably improves the effectivity of evolutionary algorithms applied to a certain class of optimization problems. The basic principle is to solve first a simpler related problem, which is constructed by introducing additional degrees of freedom to the landscape. Starting from the solution in this simplified landscape we remove stepwise the added degrees of freedom. Our optimization strategy is demonstrated for a sample problem.
Given an assembly of viscoelastic spheres with certain material properties, we raise the question how the macroscopic properties of the assembly will change if all lengths of the system, i.e. radii, container size etc., are scaled by a constant. The result leads to a method to scale down experiments to lab-size.
The onset of surface fluidization of granular material in a vertically vibrated container, z=A cos(ωt), is studied experimentally. Recently, for a column of spheres it has been theoretically found that the particles lose contact if a certain condition for the acceleration amplitude \ddot{z} \equiv Aω^2/g = f(ω) holds. This result is in disagreement with other findings where the criterion \ddot{z}=\ddot{z}_{crit}=const. was found to be the criterion of fluidization. We show that for a column of spheres a critical acceleration is not a proper criterion for fluidization and compare the results with theory.
In horizontally shaken granular material different types of pattern formation have been reported. We want to deal with the convection instability which has been observed in experiments and which recently has been investigated numerically. Using two dimensional molecular dynamics we show that the convection pattern depends crucial on the inelastic properties of the material. The concept of restitution coefficient provides arguments for the change of the behaviour with variing inelasticity.
We investigate autogenous fragmentation of dry granular material in rotating cylinders using two-dimensional molecular dynamics. By evaluation of spatial force distributions achieved numerically for various rotation velocities we argue that comminution occurs mainly due to the existence of force chains. A statistical analysis of theses force chains explains the spatial distribution of comminution efficiency in ball mills as measured experimentally by Rothkegel and Rolf. For animated sequences of our simulations see http://summa.physik.hu-berlin.de/~kies/Research/RotatingCylinder/rotatingcylind er.html
Given an equidistribution for probabilities p(i)=1/N, i=1..N. What is the expected corresponding rank ordered frequency distribution f(i), i=1..N, if an ensemble of M events is drawn?
We show that two basic mechanical processes, the collision of particles and rolling motion of a sphere on a plane, are intimately related. According to our recent findings, the restitution coefficient for colliding spherical particles ε, which characterizes the energy loss upon collision, is directly related to the rolling friction coefficient μ_{roll} for a viscous sphere on a hard plane. We quantify both coefficients in terms of material constants which allow to determine either of them provided the other is known. This relation between the coefficients may give rise to a novel experimental technique to determine alternatively the coefficient of restitution or the coefficient of rolling friction.
The transmission of kinetic energy through chains of inelastically colliding spheres is investigated for the case of constant coefficient of restitution ε=const and impact-velocity dependent coefficient ε(v) for viscoelastic particles. We derive a theory for the optimal distribution of particle masses which maximize the energy transfer along the chain and check it numerically. We found that for ε=const the mass distribution is a monotonous function which does not depend on the value of ε. In contrast, for ε(v) the mass distribution reveals a pronounced maximum, depending on the particle properties and on the chain length. The system investigated demonstrates that even for small and simple systems the velocity dependence of the coefficient of restitution may lead to new effects with respect to the same systems under the simplifying approximation ε=const.
When granular material is shaken vertically one observes convection, surface fluidization, spontaneous heap formation and other effects. There is a controversial discussion in literature whether there exists a threshold for the Froude number $Γ=A_0ω_0^2/g$ below which these effects cannot be observed anymore. By means of theoretical analysis and computer simulation we find that there is no such single threshold. Instead we propose a modified criterion which coincides with critical Froude number $Γ_c=1$ for small driving frequency $ω_0$.
The velocity distribution in a homogeneously cooling granular gas has been studied in the viscoelastic regime when the restitution coefficient of colliding particles depends on the impact velocity. We show that for viscoelastic particles the simple scaling hypothesis is violated, i.e., that the time dependence of the velocity distribution does not scale with the mean square velocity as in the case of particles interacting via a constant restitution coefficient. The deviation from the Maxwellian distribution does not depend on time monotonously. For the case of small dissipation we detected two regimes of evolution of the velocity distribution function: Starting from the initial Maxwellian distribution, the deviation first increases with time on a collision time-scale saturating at some maximal value; then it decays to zero on much larger time-scale which corresponds to the temperature relaxation. For larger values of the dissipation parameter there appears an additional intermediate relaxation regime. Analytical calculations for small dissipation agrees well with the results of a numerical analysis.
We analyze the velocity distribution function of force-free granular gases in the regime of homogeneous cooling when deviations from the Maxwellian distribution may be accounted only by leading term in the Sonine polynomial expansion. These are quantified by the magnitude of the coefficient $a_2$ of the second term of the expansion. In our study we go beyond the linear approximation for $a_2$ and observe that there are three different values (three roots) for this coefficient which correspond to a scaling solution to the Boltzmann equation. The stability analysis performed showed, however, that among these three roots only one corresponds to a stable scaling solution. This is very close to $a_2$, obtained in previous studies in a linear with respect to $a_2$ approximation.
We perform a dimension analysis for colliding viscoelastic spheres to show that the coefficient of normal restitution $ε$ depends on the impact velocity g as ε=1-γ_1g^{1/5}+γ_2g^{2/5}\mp..., in accordance with recent findings. We develop a simple theory to find explicit expressions for coefficients γ_1 and γ_2. Using these and few next expansion coefficients for ε(g) we construct a Padé-approximation for this function which may be used for a wide range of impact velocities where the concept of the viscoelastic collision is valid. The obtained expression reproduces quite accurately the existing experimental dependence ε(g) for ice particles.
The coefficient of self-diffusion for a homogeneously cooling granular gas changes significantly if the impact-velocity dependence of the restitution coefficient $ε$ is taken into account. For the case of a constant $ε$ the particles spread logarithmically slow with time, whereas the velocity dependent coefficient yields a power law time-dependence. The impact of the difference in these time dependences on the properties of a freely cooling granular gas is discussed.
We investigate collective dissipative properties of vibrated granular materials by means of molecular dynamics simulations. Rates of energy losses indicate three different regimes or "phases"in the amplitude-frequency plane of the external forcing, namely, solid, convective, and gas-like regimes. The behavior of effective damping decrement in the solid regime is glassy. Practical applications are dicussed.